Poster Paper Proc. of Int. Colloquiums on Computer Electronics Electrical Mechanical and Civil 2011 A. Random grid method Input: original image I, where I is a halftone image and the image size is 512 by 512 pixels Output: Shares S1 and S2. For(i=0;i<512;i++) For(j=0;j<512;j++) Random assign S1[i][j] as white or black If I[i][j] is white then S2[i][j]=S1[i][j]; Else S2[i][j]=complement of S1[i][j]; End if End for End for
is black, one of the last two rows in Table I is chosen randomly to encode A and B. Thus, neither A nor B exposes any clue about the binary color of p. When these two shares are superimposed together, two black sub-pixels appear if p is black, while one black sub- pixel and one white sub-pixel appear if p is white as indicated in the rightmost column in Table 1. Based upon the contrast between two kinds of reconstructed pixels can tell whether p is black or white. TABLE I. ENCODING A B INARY PIXEL P I NTO TWO SHARES A AND B USING NAOR AND SHAMIR ’ S SCHEME
VI. PROPOSED METHOD As protecting template in the database securely is one of the challenges in any biometric system. Here visual cryptography using random grids is applied to biometric authentication system . In this system there are two modules: Enrollment module and Authentication module. A. Enrollment During enrollment process, the biometric data is sent to a trusted third party entity. Once the trusted entity receives it, the biometric data is decomposed into two shares. Among these two shares one of the shares is reversed. And these two shares (one reversed) are stored in separate databases such that the identity of private data is not revealed to either server. Further, cooperation between the two servers is essential in order to reconstruct the original biometric image.
IV. VISUAL SECRET SHARING BY RANDOM GRIDS Random grid is a transparency comprising a twodimensional array of picture elements (pixels). An important property of random grids is the principle of combination. If we cut out a section from a random grid and replace it with a similar section from a second random grid, the result is yet another random grid. The number of different grids possible is of the order of 2N, where N is the number of pixels in the array. When two random grids with the same dimensions are placed one on top of the other so that they correspond pixel by pixel, the pr obabilit y of each superimposed pixel’s being transparent is ¼.Precisely, the binary secret image I with the size of h×w will be encrypted into two cipher-grids R1 and R2 with the same size as that of I as shown in fig.2. Firstly, the cipher-grid R1 is created by randomly assigning each pixel the color 0 or 1, i.e., white and black. Secondly, the other cipher- grid R2 will be created by referring both the secret image I and the ciphergrid S1 according to one of Kafri and Keren’s algorithms . Algorithm for creating the shares is explained below.
Algorithm for decomposing into two shares
Input: original image I, where I is a halftone image and the image size is 512 by 512 pixels Output: Share S1 and reverse share S2 For( i=0;i<512;i++) For(j=0;j<512;j++) Random assign S1[i][j] with subpixels If I[i][j]=white S2[512-i][j]=S1[i][j] Else S2[512-i][j]=complement of S1[i][j] End if End for End for B. Authentication Here the trusted entity sends a request to each server and the corresponding sheets are transmitted to it. Stacking these two shares will not reveal the original image, thereby improving the security. Reversing one of the share and stacking with the other will reconstruct the original private image thereby avoiding any complicated decryption and decoding computations. Only the authenticated server knows which one is the reversed share. Algorithm for superimposing two shares Input: Share S1 and reverse share S2 Output: Original image I For( i=0;i<512;i++) For(j=0;j<512;j++)
Fig. 2 Pixel table for Kafri and Keren’s first random grid algorithm
© 2011 ACEEE DOI: 02.CEMC.2011.01. 541